Mar 29, 1985 - Abstract-The instability characteristics of the bridge rectifier with input filter are described. A stability criterion based on the perturbational.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-21, NO. 6, NOVEMBER/DECEMBER 1985
1 424
Open-Loop
Instability of the Bridge Rectifier with Input Filter
EBRAHIM B. SHAHRODI,
MEMBER, IEEE, AND
Abstract-The instability characteristics of the bridge rectifier with input filter are described. A stability criterion based on the perturbational analysis is proposed. According to this criterion, the steady-stale circuit variables during stable operation are employed to examine the stability of the rectifier. Thereby, a simple and flexible stability method is developed. The method is applied to six-pulse and two-pulse bridge circuits with LC type input filter. The accuracy of the results is verified by experiment. The effects of converter output ripple, input voltage distortion, and type of gating circuit on the stability of the converter are examined experimentally and justified theoretically. Finally, the stability condition is determined explicitly in terms of the circuit parameters.
S. B. DEWAN,
L
A
FELLOW, IEEE
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I. INTRODUCTION
IN MIDRANGE- to high-power applications of power rectifiers the input filter is an indispensable part of the circuit. Input filters typically have an inductive series branch and a capacitive shunt branch in parallel with several harmonic traps. Fig. 1 shows a six-pulse bridge rectifier with an LC type input filter. The experimental results on the circuit of Fig. 1 have shown that when the synchronizing signals are taken from the converter side, the gating pulses become unstable and sustain oscillations around their operating point. The instability occurs in certain ranges of firing angles referred to here as the instability regions. During instability, the circuit waveforms become distorted, causing the following problems: 1) excessive level of ac distortion and dc ripple, 2) commutation failure of the converter when operated in the inverting mode, 3) large swing of reactive power in high-power installations, 4) overheating, stalling, and impairment of dc motors in dc drives, 5) overheating of transformers, inductors, capacitors, and generators, 6) activation of the converter protective elements. In most stability studies of the literature, closed-loop converters are considered. The destabilizing effect of the line inductance has been studied in [1] where the instability is defined as the unusual magnification of one of the ac harmonics due to irregularity of the gating pulses. In [2], the describing function method has been used to derive the conditions for the sustenance of subharmonic oscillations Paper IPCSD 85-24, approved by the Static Power Converter Committee of the IEEE Industry Applications Society for publication in this Transactions. Manuscript released for publication March 29, 1985. The authors are with Inverpower Controls Ltd., 835 Harrington Court, Burlington ON, Canada L7N 3P3.
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raised during instability in a closed-loop converter system (without the input filter). A review of the stability studies of the literature is given in [3]. The majority of these methods are small signal approximate methods based on the following assumptions: a) the output current of the converter has no ripple; b) the converter output current remains unchanged during the instability; c) the converter input voltage is distortionless; d) the converter input voltage has a fixed amplitude and phase angle. It is shown, in this paper, that these assumptions are not always justifiable for the circuit of Fig. 1; the fourth assumption is not valid at all. Therefore, a stability criterion suitable for the rectifiers with input filter is developed. In Section II of this paper, the instability characteristics of the rectifier with input filter is described based on experimental results. The effects of the power filter and traps, the type of gating circuit and its filter, and the converter load parameters
are examined. In Section III the describing function method is used to justify qualitatively some of the instability characteristics of the rectifier with input filter. The perturbational stability criterion is developed in Section
0093-9994/85/1100-1424$01 .00 © 1985 IEEE
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SHAHRODI AND DEWAN: OPEN-LOOP INSTABILITY OF THE BRIDGE RECTIFIER
IV. It is followed by several illustrative examples justifying the experimental results of Section II. Employing the criterion, the instability regions of the bridge rectifier are explicitly determined in Section VI. II. INSTABILITY CHARACTERISTICS OF THE BRIDGE RECTIFIER WITH INPUT FILTER In this section, experimental results are used to describe the
characteristics of the bridge rectifier with input filter (Fig. 1) during instability. The effects of circuit parameters and configuration on the stability are also examined. Initially, the circuit parameters are held at the values shown in Fig. 1. The results of experiment on the circuit of Fig. 1 show that the gating pulses become unstable at certain values of the firing angle. During the instability, the gating pulses oscillate around their operating point, thus distorting the waveforms of the circuit variables (Fig. 2). If the gating circuit is the individual phase-control, the gating pulses do not remain equidistant. The spectrum analysis of the rectifier input voltage (Fig. 3) shows that, during instability, some components at frequencies lower than the fundamental frequency emerge. The sustenance of the subharmonic of order two is seen in Fig. 3. The results of experiments indicate that the frequency and amplitude of gating pulse oscillations are closely related to the frequency and amplitude of the low-frequency signal. Another notable effect of instability is a sudden shift of the gating pulses from one stable point to another. This effect is referred to here as the jump effect.
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In the following sections, the foregoing characteristics are examined in connection with the power and gating circuit structures. a) LC Filter Parameters: The reduction of the series inductance L causes the instability regions to diminish, and if L is small enough, the circuit remains stable over the entire range of firing angles. In contrast, the filter capacitor has little effect on the stability; the variation of the filter capacitance shifts the instability regions with no substantial reduction in the regions of instability (Fig. 4(a)). b) Equidistant Gating Circuit: The operation of a microprocessor-based equidistant gating circuit is described in [4]. The circuit requires one synchronizing zero-crossing every cycle. Employment of this gating circuit during the stability study of the circuit of Fig. 1 shows that no substantial improvement in the stability is made except for some reduction in the harmonic content of the variables. c) Low-Pass Filter for the Gating Circuit: In order to
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pp. 139-152, Jan. 1967.
[31 J. 0. Lagasse and R. Prajoux, 'Behaviour of control systems including controlled converters, especially rectifiers: A review of existing theories," in Proc. IFAC Symp., vol. 2, 1974, pp. 1-38. [41 E. B. Shahrodi, "Six-pulse bridge ac/dc converters with input filter,"
Ph.D. dissertation, Univ. of Toronto, Toronto, ON, Canada, 1983. [51 W. McMurray. "Stability theory of converters with counter EMF load," in Proc. U.S.-Japan Conf. S5.1, 1981, pp. 159-168. [6] A. Balestrino et al., "On the stability of thyristor phase-controlled converters," in Proc. IFAC Symp., vol. 1, 1974, pp. 1-16. [7] E. B. Shahrodi and S. B. Dewan. "Steady state characteristics of the six-pulse bridge rectifier with input filter," in Proc. Annu. IEEE Conf. Ind. Appl., 1984, pp. 840-846.
Ebrahim B. Shahrodi (M'84), for page 1423 of this issue.
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photograph and biography please
S. B. Dewan (S'65-M'67-SM'78-F'82). for please see page 1423 of this issue.
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photograph and biography
